Showing papers on "Bessel filter published in 1985"

On the exceptional zeros of cross-products of derivatives of spherical Bessel functions

Abstract: The lowest zeros of the cross-products of derivatives of spherical Bessel functions are not obtainable from a McMahon-type formula. This paper derives an analytical approximation for these lowest, “exceptional”, zeros, through to 4th order in a parameter specifying the thinness of the corresponding concentric spherical region.

Bessel transforms and rational extrapolation

Abstract: A numerical method is developed which handles the Bessel transform of functions having slow rates of decrease. The method replaces the Bessel transform by a related damped transform for which the sinc quadrature rule provides an efficient and accurate approximation. It is then shown that the value of the original Bessel transform can be obtained from the damped transform by extrapolation with the Thiele algorithm.

Bessel Delay Networks for Population Models

Abstract: BESSEL networks are proffered instead of customary cascaded, first-order delay networks for representing transit times or delays of age-classes in population system models. An impulse response with specified coefficient of variation is obtained by a Bessel network about half the size of a cascaded, first-order network. Consequently, up to 50% fewer system equations are required with Bessel networks—a significant saving for complex population systems. System analysis of models containing Bessel networks is readily accomplished by state variables methods. Theory of Bessel network representation of age-class delay, synthesis and comparative performance of these networks, and method of application are presented.

Some design methods for two‐dimensional digital filters with complex coefficients in consideration of linear phase characteristics

Abstract: In designing a two-dimensional digital filter with special consideration of the phase characteristics, particularly the group delay characteristics, a very high-order filter is generally required. This paper extends the coefficients of the filter from real to complex and describes a design technique for comparatively low-order, two-dimensional, circularly symmetric filters with consideration of phase characteristics. First, the method of transforming a two-dimensional input signal into an analytic signal is described and then the design technique of two kinds of complex coefficient filters which use the properties of analytic signals is discussed. In the first kind variable transformation to a 1-D real coefficient FIR filter is used to obtain a 2-D FIR filter with complex coefficients. It has the merits of permitting independent setting of the sharpness of cutoff characteristics and circular symmetry. In the other kind of complex coefficient filter a recursive digital filter is obtained by using an all-pole filter having constant group delay in the passband of the transfer function and having a 2-D complex coefficient mirror image polynomial. It always has a constant group delay unrelated to the values of the coefficients and the overall group delay is also constant. Moreover, in this paper, design examples based on these methods are given and the validity of our methods is shown.